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The paper concerns the design of locally optimum data receivers for dispersive non-Gaussian channels. A number of approaches are considered for the optimisation of the receiver when the detection is carried out either on a bit-by-bit or a block basis. A number of interesting receiver structures are shown to result when the design is carried out (a) by assuming the knowledge of adjacent bits (decision-feedback approach), (b) by composite hypothesis testing, or (c) by the maximum likelihood sequence estimation approach. Although the design here has been carried out using baseband signal representations, it should be possible to obtain similar results for bandpass modulations. Performance characteristics of these receiver structures based on bounds on the error probability have also been presented. Numerical evaluation of the error probability is carried out for a lowpass symmetric impulse response channel in the presence of a generalised Gaussian noise. Comparison of the numerical results for different receivers yields some interesting insights into the relative performance of the various receivers.